A transformation theorem for one-dimensional F-expansions

1973

Applied Mathematics Letters, 2008

The present work presents some necessary and sufficient conditions for the convergence to a periodic function of a special kind of function series defined by ∞ j=0 f (t − jd), where f : R → R + ∪ {0} with f (t) = 0 for t < 0. It also discusses some biological applications that can be derived from these results, by considering each f (t − jd) as describing an isolated effect related to an application at time jd, and the sum of them as an accumulated effect.

2003

Let (X, d) be a compact metric space, and let an iterated function system (IFS) be given on X, i.e., a finite set of continuous maps σi: X → X, i = 0, 1, • • • , N − 1. The maps σi transform the measures µ on X into new measures µ i. If the diameter of σi 1 • • • • • σi k (X) tends to zero as k → ∞, and if pi > 0 satisfies i pi = 1, then it is known that there is a unique Borel probability measure µ on X such that µ = i pi µ i (*) In this paper, we consider the case when the pis are replaced with a certain system of sequilinear functionals. This allows us to study the variable coefficient case of (*), and moreover to understand the analog of (*) which is needed in the theory of wavelets.

2009

In the note, the complete monotonicity of difference between remainders of Binet's formula and the star-shaped and subadditive properties of the remainder of Binet's formula are proved.

Colloquium Mathematicum, 2013

A generalization of the weighted quasi-arithmetic mean generated by continuous and increasing (decreasing) functions f1,. .. , f k : I → R, k ≥ 2, denoted by A [f 1 ,...,f k ] , is considered. Some properties of A [f 1 ,...,f k ] , including "associativity" assumed in the Kolmogorov-Nagumo theorem, are shown. Convex and affine functions involving this type of means are considered. Invariance of a quasi-arithmetic mean with respect to a special mean-type mapping built of generalized means is applied in solving a functional equation. For a sequence of continuous strictly increasing functions fj : I → R, j ∈ N, a mean A [f 1 ,f 2 ,...] : ∞ k=1 I k → I is introduced and it is observed that, except symmetry, it satisfies all conditions of the Kolmogorov-Nagumo theorem. A problem concerning a generalization of this result is formulated.

Acta Mathematica Academiae Scientiarum Hungaricae, 1955

Http Digital Bl Fcen Uba Ar, 2011

has received special interest from the applications. In some way, this representations resemble the classic Karhunen-Loève theorem [27]. A property of the Karhunen-Loève expansion of a random process is that one obtains an orthonormal basis of the closed linear span of the whole process. This allows to write certain approximations as unconditional convergent series. This useful property could be obtained under other conditions. To solve this problem, nally, we study conditions under which a stationary sequence forms a frame or a Riesz basis of its closed linear span.

The Ramanujan Journal, 2015

We give two general transformations that allows certain quite general basic hypergeometric multi-sums of arbitrary depth (sums that involve an arbitrary sequence {g(k)}), to be reduced to an infinite q-product times a single basic hypergeometric sum. Various applications are given, including summation formulae for some q orthogonal polynomials, and various multisums that are expressible as infinite products.

Electronics and Communications in Japan (Part III: Fundamental Electronic Science), 1992

Given an absolutely square-integrable waveform bandpass limited to the interval 1 o 1 s o,, o, > 0, and regularly spaced sample points t,, = nrO. (1-0 = x/ol, o, > 0 , ; n = 0, f 1, f 2 , ...), the interpolation formula theorem is determined which minimizes the above-mentioned measure of the interpolation functions. Using these arguments, we also derive generating functions which minimize various weighting measures related to the interpolation functions $,(t), such as when the weights are squares, (2k)-th powers, and (1 + n'r?).

Fuzzy Sets and Systems

Let I ⊂ (0, ∞) be an interval that is closed with respect to the multiplication. The operations C f,g : I 2 → I of the form C f,g (x, y) = (f • g) −1 (f (x) • g (y)) , where f, g are bijections of I are considered. Their connections with generalized weighted quasi-geometric means is presented. It is shown that invariance question within the class of this operations leads to means of iterative type and to a problem on a composite functional equation. An application of the invariance identity to determine effectively the limit of the sequence of iterates of some generalized quasi-geometric mean-type mapping, and the form of all continuous functions which are invariant with respect to this mapping are given. The equality of two considered operations is also discussed. C f,g (x, y) = (f • g) −1 (f (x) • g (y)) ,